The nanoparticles have a huge tendency to weld with each other in the solid state and form larger particles to reduce the total surface energy the system. Thus, measuring their melting point (MP), which requires heating, before their growth becomes a challenge.

Different approaches have been developed to measure the MP of nanoparticles including:

1- Measuring the MP while the nanoparticles dispersed on a surface of inert substrate, however, the effect of the adsorption must be eliminated in such approach. Moreover, such approach requires very high heating rates, thus, the MP is NOT measured in the equilibrium conditions. Also, measuring the MP of an exact size is NOT possible here.

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2- Measuring the MP under the TEM using the electron beam as heating source. In such case, the measured MP point is specific for a given size, however, it is measured under the low pressure required to operate the TEM.

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Valuable information regarding the melting-point depression is available at:

https://en.wikipedia.org/wiki/Melting-point_depression#cite_note-Allen-7

A simple method would be use of 'nano' differential thermal analysis or differential scanning nano-calorimetry (nano DSC). Reliability and accuracy of the data are separate issues to deal with. The data need to be analyzed based on the surface energy considerations as discussed by Imad Disher.